Recently, I've been working on two different Starfinder games, one I'll be running live on Discord and one here on The Tangled Web. As I've been prepping those games, I've been thinking about the differences in Dming those styles of tabletop playing. The following are just my thoughts on how those formats of playing differ and how they're similar.

Pacing

Forum based play by post is inherently a slow paced medium. It's designed for those who don't have a lot of free time or anyone close to play with, but still want that taste of playing Dungeons and Dragons. Usually most players only post a few times a week once the new game hype has faded. Currently, my longest running game (Rookie Card) has the players at Level 4 (5 after this quest finishes) after almost 3 years of playing. While I may be slower than some play by post DMs, this does seem to be pretty usual for play by post.

Using Discord or another service to play an online game through voice chat does mean for a much faster play speed. Players tend to take less time to complete questlines. This makes for a much faster pacing, even with short sessions. Mine tend to be 2 hours or less, though I have run IRL games that were about 5 hours per session. My longest running party will have been running for 1 year in a few weeks (January 2019 for the READERS FROM THE FUUUTUUURE) and are close to reaching level 8. This is even true for play by post Discord games. A LmoP (Lost Mines of Phandelver) game I've been playing in has reached Level 2 in less than 2 months.

Player Drop

Players drop. This is an unfortunate fact of Dming. But how and why they drop between mediums is vastly different.

While sometimes Play by Post players will message their Dms and give a reason (sometimes a weak/lame one) why they're dropping, far more players have been lost to simply Ghosting, or them just stopping playing altogether.

Live/ Discord players tend to warn you when they drop. This is often due to scheduling conflists such as classes or work.

Open World or Module to the Max

Open world games can be a lot of fun, both for the Dungeon Masters and the players. But they can present a series of unique challenges for Play by Post.

Open World games tend to fade quickly on Play by Post. Play by post requires a certain amount of structure and planning to be sucessful. This makes modules very successful on forum based play by post. Even looking around on this forum, you can see quite a few modules or adventure paths being played through.

Open world is much easier to run on a voice chat app. The party can confer and play of each other. This makes exploration and adventuring much easier. Modules can also work quite well through voice chat or a pbp through discord or another voice service. It's more a question of how well open world/ exploration games work in a purely play by post setting.

Character Interaction.

Character interaction between player characters feels incredibly different between play by post and live games.

Character interaction on a play by post game consists entirely of reading the Dms and your fellow PCs, then reacting to it with a post of your own. This can be as simple as a single sentence or as involved as several paragraphs that stretch the textbox to its breaking point. This does mean that sometimes that you and another PC post that you want to do the same or a similar action at the same time, then one of you has to edit their post or delete it. It's also possible to lose long involved posts due to an internet glitch or the site being obstinate. For those, it's best to write in an offline word processor like LibreOffice, Word, OpenOffice, etc then post into the text. A number of pbp players like to use colored lettering to denote dialouge or different languages. One main challenge I see is with those who are weaker with the sites primary language decoding the sometimes walls of text.
Character interaction through a live game is entirely different. You're talking to a live person and are able to interact with their characters decisions in real time. This can mean it's easy to be derailed or make terrible puns. You also have the added hazard of navigating the perils of online voice chat which can lead to a number of frustrating moments when you “Robot” or drop. It can also be more difficult to find that window of uninterrupted quiet and privacy to join a voice call for several hours. It can be the superior experience when everything is working correctly.

Quest Planning

If you're a homebrewer like me, you probably spend a lot of time working on quests, NPCs and background elements of your world. How you build quests can radically vary.
For building a quest for Play by Post, I tend to build fewer quests but with more details and stages. Since these quests can take a long time to complete, you want plenty of content in your quests. I also think it's best to have all the steps of your quests plotted out in advance. If your players do go off the rails, it's pretty easy to rebuild the structure. Dungeon crawls tend to work well in play by post.
When I'm building for live games, I tend to make more, less detailed quests, sometimes with an overarching story. You do want to give your players some freedom and choice in live games. It's possible to run live with nothing but a encounter chart and plenty of creative and fun descriptions. You do want to prep some stuff ahead of time, namely treasure, since most players hate downtime and dead air. Your players might decide mid session that they want to take a different route or go another place altogether. Give yourselves some freedom and some options when making live quests.

That's all the thoughts I have on PbP and live game differences. Now, if you'll excuse me, I have some Starfinder games to work on.